Quantum Mechanics of Complex Systems, I

Abstract

Very often in physics and chemistry we are interested in the motion of some variable which is described by quantum mechanics and is strongly coupled to an “environment,” that is, one or (more likely) many other variables whose behavior is of no particular interest to us in its own right, but only because of the effect it may exert on the motion of the “system,” that is, the variable of primary interest. Some familiar examples of such “systems,” with the “environment” indicated in parentheses, are an electron participating in a chemical reaction (the vibronic modes), a paraelectric defect in a solid, such as OH- in KCl, (phonons), a μ-meson in a metal (conduction electrons) and the \(\rm{K_O-\bar K_O}\) system (surrounding matter). All these are old problems. A class of problem which is of rather more recent interest is when the “system” variable is in some sense macroscopic: examples include charge density waves (normal electrons), the magnetization of small ferromagnetic particles (magnons, phonons), the early Universe (preexisting mesons) and, par excellence, the phase of the Cooper pairs in devices incorporating one or more Josephson junctions (normal electrons, phonons, radiation field, nuclear spins …). The last example has been studied intensively both experimentally and theoretically over the last few years and provides probably the best test-bed for ideas in this area. One further example which is of great current interest is the quantum tunnelling motion of a pair of deuterium nuclei in a matrix of a metal such as Pd or Ti; in this case the “environment” is the conduction electrons, the nuclei of the metal and any “third-party” deuterons which may be present.